Table 1.

Results of PAML random sites models for Rh2 in New World warblers, Old World warblers and across Passerines, based on the main dataset, consisting of full opsin sequences. Likelihood ratio tests (LRT) were performed to test whether two more parameter rich models, M2a and M8, that allow for a category of positively selected sites, fit the data better than their nested, simpler counterparts, M1a and M7 respectively. The resulting test statistic was compared to a ${\chi }_2^2$ distribution both in the M2-M1a and M8-M7 comparison (Yang et al. 2000). Positively selected sites identified by Bayes Empirical Bayes factors (BEB) are shown. M0: One-ratio model; M1a neutral model, M2a: selection model; M7: Beta; M8:Beta+ω (Yang et al. 2000). ω= d_N/d_S

Clade	Model	lnL	np	Parameter Estimates	Sites Identified by BEB	p- value (LRT)
New World warblers	M0	−1891.15	31	ω0=0.055	-
	M1a	−1876.65	32	p0= 0.9999, ωo=0.00001	-	NS (0.14)
	M2a	−1874.68	34	p0= 0.978, ωo=0.000, p2= 0.022, ω2=2.731	7 85 284 332
	M7	−1879.64	32	p= 0.0097, q= 0.163	-	0.006
	M8	−1874.68	34	p0= 0.978 (p1=0.022), ω=2.731	7 85 284 332
Old World Warblers	M0	−1705.44	17	ω0=0.0086	-
	M1a	−1705.44	18	p0=0.9999, ωo=0.0086	-	NS (0.99)
	M2a	−1705.44	20	p0=1.00,ωo=0.0086, p2=0.00, ω2=1.00	none
	M7	−1705.48	18	p=0.90, q= 99.0	-	NS (0.99)
	M8	−1705.49	20	p0=0.999 (p1=0.001), ω=1.00	none
Passerines (Main dataset)	M0	−3459.64	66	ω0=0.017	-
	M1a	−3428.71	67	p0=0.979, ωo=0.01	-	NS (0.99)
	M2a	−3428.71	69	p0=0.979,ωo=0.01, p2=0.021, ω2=1.00	332
	M7	−3419.74	67	p=0.06, q= 2.07	-	0.001
	M8	−3412.92	69	p0=0.0994 (p1=0.006), ω=1.64	332

lnL the log value of the model’s likelihood score given the data and phylogeny.

NS = non-significant

np = number of parameters.

p_i is the proportion of sites in each category.

p and q are shape parameters for the Beta distribution.